# Properties

 Label 3234.2.x Level 3234 Weight 2 Character orbit x Rep. character $$\chi_{3234}(491,\cdot)$$ Character field $$\Q(\zeta_{10})$$ Dimension 656 Sturm bound 1344

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$3234 = 2 \cdot 3 \cdot 7^{2} \cdot 11$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 3234.x (of order $$10$$ and degree $$4$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$33$$ Character field: $$\Q(\zeta_{10})$$ Sturm bound: $$1344$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(3234, [\chi])$$.

Total New Old
Modular forms 2816 656 2160
Cusp forms 2560 656 1904
Eisenstein series 256 0 256

## Trace form

 $$656q + 4q^{3} - 164q^{4} - 5q^{6} + 8q^{9} + O(q^{10})$$ $$656q + 4q^{3} - 164q^{4} - 5q^{6} + 8q^{9} - 6q^{12} + 12q^{15} - 164q^{16} - 5q^{18} - 30q^{19} + 5q^{24} + 180q^{25} - 26q^{27} + 30q^{30} + 38q^{31} - 47q^{33} - 12q^{34} - 7q^{36} + 36q^{37} + 50q^{39} - 10q^{40} - 8q^{45} - 20q^{46} + 4q^{48} + 25q^{51} - 20q^{52} - 4q^{55} - 45q^{57} + 30q^{58} - 8q^{60} + 60q^{61} - 164q^{64} + 20q^{66} - 68q^{67} + 42q^{69} + 20q^{72} + 30q^{73} + 23q^{75} + 80q^{78} + 20q^{79} + 20q^{81} + 14q^{82} - 60q^{85} + 90q^{90} + 42q^{93} - 80q^{94} - 14q^{97} - 146q^{99} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(3234, [\chi])$$ into newform subspaces

The newforms in this space have not yet been added to the LMFDB.

## Decomposition of $$S_{2}^{\mathrm{old}}(3234, [\chi])$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(3234, [\chi]) \cong$$ $$S_{2}^{\mathrm{new}}(33, [\chi])$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(66, [\chi])$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(231, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(462, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(1617, [\chi])$$$$^{\oplus 2}$$

## Hecke characteristic polynomials

There are no characteristic polynomials of Hecke operators in the database